On quantum group SLq(2)

Joseph Bernstein, Tanya Khovanova

Abstract

We start with the observation that the quantum group SLq(2), described in
terms of its algebra of functions has a quantum subgroup, which is just a
usual
Cartan group.

Based on this observation we develop a general method of constructing
quantum groups with similar property. We also describe this method in the
language of quantized universal enveloping algebras, which is another common
method of studying quantum groups.

We carry our method in detail for root systems of type SL(2); as a byproduct
we find a new series of quantum groups - metaplectic groups of SL(2)-type.
Representations of these groups can provide interesting examples of bimodule
categories over monoidal category of representations of SLq(2).